How do we know that the speed of light is the same everywhere in the universe?

What observations can we make that disprove that c has a different value in say GN-z11?

The speed of light in a vacuum is constant. That “in a vacuum” qualifier is important. Light slows down when it passes through something like glass or water, for example.

Maxwell’s equations and Einstein’s theory of special relativity end up giving us a speed of light that is constant. Maxwell started with the theory that electromagnetic waves propagated at the same speed as light, and took it a step further to theorize that light itself was an electromagnetic wave. Einstein’s theory of special relativity is based around the speed of light being constant, at least in a vacuum. This gets carried further into Einstein’s general relativity as well.

We can’t easily measure the speed of light in someplace like the middle of GN-z11, but we can bounce lasers off of objects at various distances and measure the time it takes for the laser beam to go there and come back. So far, all of our measurements confirm a constant speed of light, and other predictions that result from Maxwell and Einstein have also been consistent with our observations.

The issue isn’t every where it’s every time.

If the speed of light differed noticeably somewhere else there would be large ramifications in terms of galaxy and star formation, properties, etc.

There’s some suggestions that due to expansion of the Universe, the speed of light might vary due to the vacuum not being a vacuum.

Various similar ideas have also been proposed to suggest that the speed of light was slightly different in the early-ish days of the Universe. And perhaps seriously different in the very earliest moments as an alternative to inflation.

Well to be exact it is the speed of Causal connectivity or causality and not light. Light is massless and everything without mass travels at the speed of light (in a vacuum).

Einstein created the theory special relativity by guessing that the speed of light is constant in all inertial frames. The framework of relativity is based on the hypothesis of a universal speed limit and depends on a universal speed limit.

Based on this assumption special relativity predicted other phenomenon is testable with experiments. In addition almost every modern theory of physics is based on that theory and those theories have predicted all sorts phenomenon that Einstein may never have thought about and the accuracy of those predictions is staggering.

We’ve never been able to perform an experiment that conclusively shows that the speed of light isn’t constant in every inertial frame, and every experiment we have thought up fails to contradict the other predictions from Einstein’s theory.

Had his other predictions, or the predictions of theories based on it failed it wouldn’t have been accepted.

If we ever do find evidence that contradicts a constant speed of light the notion will be considered incomplete or false depending on the nature of the evidence.

We don’t know that, because we cannot observe and measure that speed everywhere.

But the theory that it is constant in a vacuum, as noted above, is consistent with all known observations to date. Since we are unlikely to go measure the speed of light in GN-z11 anytime soon, that’s as good as we’re going to get.

I’d say it’s even a bit more than that. A heck of a lot of physics theory uses the constant C. It’s the speed of not just light but also of gravity and information transfer. You can measure the value of this constant by a dozen completely different experiments that have nothing to do with light at all.

It’s not just that we’ve measured the speed before and it seems to be the same; it’s that if this value is not a constant but in fact can change, lots and lots of physics would be quite broken.

Perhaps another way of thinking about it is this. The speed of causality in any useful metric is exactly one. Time progresses at exactly one second per second, and relativity tells us what we see when things move in space and how that relates to the passage of time. What we measure as c is a byproduct of the mechanisms by which we measure things relative to that speed. How we define a second and how we define a metre. They come about from other physical constants that are orthogonal to c (at least as far as current theory takes us they are not dependant upon c.) To say that c is different in some other part of the universe would be the same as saying that these other physical constants have a different value. That has significant implications for physics in that other part of the universe. Some constants are so finely balanced that the physical environment we take for granted won’t work. Atoms cease to be able to exist, sub-atomic physics stops working the same. The fact that we observe far away galaxies at all puts some extraordinary tight bounds on the physical constants that are in sway.

So, what are some specific observations that are inconsistent with the universal constant c varying from place to place?

That is, something along the lines of, “If c varied from place to place, we would expect to see X, but we when we look, we don’t see X.”

Well, for one, if the speed of light was different in those distant places where we have observed supernovae, we would either:

Observe that light arriving here at a different speed from our local light, or…

(if the light had changed speed in transit to match ours) observe the supernova phenomenon playing out at the wrong speed - like playing a video tape at the wrong speed

Well, for one, if the speed of light was different in those distant places where we have observed supernovae, we would either:

AFAIK, the speed of light arriving in a telescope is not usually measured. I also don’t think that the different physical laws of another part of the universe could be “carried over” to us.

If a car is manufactured on an assembly line in Detroit every hour, gets on the freeway and races to Chicago, then one car per hour will enter Chicago. In other words, the observed rate won’t change. Neither do I think we know the speed at which a supernova happens to any great accuracy.

To answer the OP:
We observe for almost every object in the universe a redshift of its light reaching us, and this redshift depends only on the objects distance to us.
I think a different fundamental speed along the way would influence the redshift, and it would be a highly specific arrangement if this just happened to be the same for every object.

(Now for the wild speculation: There is something called the Sachs-Wolfe effect. Maybe one could do the same assuming a variation in c? )

If we observe a supernova we can be pretty damn sure the physicals constants there are the same as here. If they varied, there would likely be no nova to observe, indeed stars would not be possible or even atoms. The simple reality that we are observing things that we understand the physical processes of in a pretty detailed manner - such as we can get spectra from faraway objects and determine the presence of known elements - tells us that physics is working the same as ours to a very very high degree of precision.

Fundamentally, the only constants it makes sense to talk about varying from place to place, or with time, are the unitless ones. We could, for instance, ask if the ratio of the mass of the electron to the mass of the proton is the same everywhere, or the Fine Structure Constant. And occasionally, someone does in fact propose a hypothesis that one of these numbers is different somewhere or somewhen else (though these hypotheses never actually pan out). But for a number with units, you have to ask what you’re comparing it to.

If the fine structure constant changes, it will change the frequency of the spectral lines of all atoms. When we look at distant galaxies, their spectra are, of course, different. We interpret this as the Doppler shift, due to recession of those galaxies.

I heard Fred Hoyle give a talk in the 1970’s, long after his steady-state theory had been defeated by the Big Bang theory. As recall, he had a theory in which the fine structure constant depended on time and space. This led to red shifts when looking at distant galaxies that were caused by the different value of the fine structure constant.

If you want to think of that as the speed of light changing and everything else being constant, be my guest. As Chronos mentions, the only physically meaningful thing to talk about is changes in unit-less numbers.

More recently, other cosmological models have been proposed in which the fine structure constant changes in time (see John Moffat, for example). As far back as the early days of quantum theory, Dirac proposed that gravity has been getting steadily weaker than electromagnetism (Dirac’s large number hypothesis), so that the 40 or so orders of magnitude difference in the strength between an electron and proton was attributed to the 40 or so orders of magnitude of the ratio of the age of the universe to the orbital period of the electron around a proton in a hydrogen atom (or something like that). People have done laboratory experiments to test whether any change in the fine structure constant can be observed over a period of months or years. These experiments have ruled out the changes predicted by Dirac’s hypothesis.